You could try running the plugin through steam as a non-steam game, it may work when another steam game is running, or maybe try changing the desktop mode input configs in steam->settings->controller to send regular controller inputs. These are just hunches, I dont have a steam controller to test it myself
Tested it out. Added as a non-steam game and it gets detected as an xbox controller and works when the Nyarupad program is clicked on and active. But once I click onto a different window application like another game or browser, then it stops sending button inputs it Vtube Studio. Works again once I click back to Nyarupad as an active window again though. But stops work as soon as i click something else.